MATHDLL_API Vector3 RotateAround(const Vector3 & axis, float amount, const Vector3 & vectorToRotate)
{
Matrix4 identity;
identity.Identity();
Matrix4 first = identity * cos(amount);
Matrix4 second = TensorProductMatrix(axis) * (1 - cos(amount));
Matrix4 third = CrossProductMatrix(axis) * sin(amount);
Vector4 endVal = (first + second + third) * vectorToRotate;
return Vector3(endVal.x, endVal.y, endVal.z);
}
void FlyingLayer::AngleAxisRotationMatrix(float angle, const Vector3f& axis, Matrix3x3f &retval) const {
Vector3f axisVec = axis.normalized();
// use Rodrigues' formula to create the matrix
float cos_angle = std::cos(angle);
float sin_angle = std::sin(angle);
// start with the cross product term, calculating it in-place
CrossProductMatrix(axisVec*sin_angle, retval);
// add Matrix3x3f::Identity()*cos_angle to retval
retval(0, 0) += cos_angle;
retval(1, 1) += cos_angle;
retval(2, 2) += cos_angle;
// add the outer product term -- multiply the scalar factor before forming the outer product
retval += ((1.0 - cos_angle)*axisVec) * axisVec.transpose();
}
Matrix3x3f FlyingLayer::CrossProductMatrix(const Vector3f& vector) const {
Matrix3x3f result;
CrossProductMatrix(vector, result);
return result;
}
EigenTypes::Matrix3x3f MathUtility::CrossProductMatrix(const EigenTypes::Vector3f& vector) {
EigenTypes::Matrix3x3f result;
CrossProductMatrix(vector, result);
return result;
}
